Aeroelastic Analysis of Rotor Blades with Elastic Restraint

Aeroelastic analysis of helicopter rotor blades has always remained a key issue in the field of helicopter dynamics research. At present, studies on rotor blades focus mostly on classical boundary conditions. However, the elastic restraint better aligns with the actual connection status of the rotor blade root. In this paper, an aeroelastic coupling dynamic model of a rotating helicopter rotor blade subjected to elastic restraint is established based on the Hamilton principle to study the influence of boundary conditions on the aeroelastic response of the rotor blade. The coupling effects between lead–lag, flapping, and torsional motions are considered simultaneously in this model. The penalty function method is employed to address elastic restraints, enabling flexible adaptation to arbitrary boundary conditions by adjusting penalty factors. The ranges of these penalty factors corresponding to elastic restraint are determined through structural frequency analysis. The aerodynamic loads are calculated through the quasi-steady Greenberg aerodynamic theory and the Dress inflow model. The modified Fourier series is employed to expand the displacement field to obtain the aeroelastic governing equation in matrix form. The accuracy of the proposed model is validated by comparing the frequency obtained by the structural dynamics equation of the rotor blade with published results. The coupled aeroelastic governing equation is numerically resolved by combining the Newton–Raphson method and the Newmark method, thereby enabling an aeroelastic response analysis. Additionally, the correlation between the constraint spring stiffness and aeroelastic response is studied through parametric variations. The results show that under both rotating and non-rotating conditions, the frequencies of lead–lag, flapping and torsional modes increase with the corresponding increasing spring stiffness and significantly change in the intervals corresponding to the elastic restraint. Furthermore, the displacement and vibration amplitudes of the rotor blade are amplified in the direction where the boundary constraint weakens.